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Indirect Geoeconomic Influence: A Switching Dynamical Systems Framework for Mechanism Design
Nikolos Gurney, Boxi Fu, Soham Hans, Volkan Ustun
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 93%
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Summary
The paper introduces a formal framework for Indirect Geoeconomic Influence (IGI) using Switching Dynamical Systems (SDS). It models how a sender state engineers a target's internal political economy to generate compliance pressure, rather than mandating policy directly. The framework distinguishes between a 'permissive mode' (before detection) and a 'contested mode' (after detection), with the transition between them shaped by the sender's mechanism design. A combinatorial optimizer searches a 'switch vector' of design dimensions to identify high-performing mechanism archetypes.
Entities (10)
Relation Signals (6)
Indirect Geoeconomic Influence → modeledby → Switching Dynamical Systems
confidence 95% · The framework rests on a switching dynamical system (SDS) in which a target's political economy evolves under mode-dependent rules.
Combinatorial Optimizer → searches → Switch Vector
confidence 94% · a combinatorial optimizer searches this space for high-performing archetypes
Sender → uses → Switch Vector
confidence 93% · A structured switch vector decomposes any mechanism along discrete design dimensions... the sender's switch vector shapes when the target enters a resistant regime
Target → transitionsfrom → Permissive Mode
confidence 92% · a permissive mode, in which a mechanism transmits pressure... and a contested mode, entered naturally once the target detects and attributes the mechanism.
Target → transitionsto → Contested Mode
confidence 92% · a contested mode, entered naturally once the target detects and attributes the mechanism.
Legibility → influences → Transition to Contested Mode
confidence 88% · the sender's mechanism design shapes the transition into the contested mode... the legibility penalty is scaled by the salience of the government channel
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Abstract
Abstract:We develop a formal framework for analyzing indirect geoeconomic influence. The influencing state (sender) does not attempt to change a target nation's policy directly. Instead, the sender restructures the target's internal political economy so that its own citizens, firms, and institutions generate the compliance pressure. The framework rests on a switching dynamical system (SDS) in which a target's political economy evolves under mode-dependent rules. We analyze two modes: a permissive mode, in which a mechanism transmits pressure toward the sender's preferred policy, and a contested mode, entered naturally once the target detects and attributes the mechanism. Crucially, the sender's mechanism design shapes the transition into the contested mode rather than paying a static toll for legibility. This inverts the usual regime-switching problem: rather than estimating a latent transition kernel from data, the designer engineers the kernel to steer regime occupancy over a planning horizon. A structured switch vector decomposes any mechanism along discrete design dimensions, and a combinatorial optimizer searches this space for high-performing archetypes scored on compliance, time-to-threshold, and a durability ratio. We characterize mode-conditional equilibria and derive comparative statics on credibility and legibility, showing that the legibility penalty is scaled by the salience of the government channel and therefore interacts with the mechanism's cost incidence. We illustrate the framework with two stylized mechanisms, report a proof-of-concept simulation over a reduced switch space, and report a small blind-audit study of the pipeline's optional language-model generation stage.
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- Source: https://arxiv.org/abs/2608.07940v1
- Canonical: https://arxiv.org/abs/2608.07940v1
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Indirect Geoeconomic Influence: A Switching Dynamical Systems Framework for Mechanism Design Nikolos Gurney Thanks: Corresponding author: gurney@ict.usc.edu Boxi Fu Soham Hans Volkan Ustun Institute for Creative Technologies, University of Southern California 07 August, 2026 Abstract We develop a formal framework for analyzing indirect geoeconomic influence. The influencing state (sender) does not attempt to change a target nation’s policy directly. Instead, the sender restructures the target’s internal political economy so that its own citizens, firms, and institutions generate the compliance pressure. The framework rests on a switching dynamical system (SDS) in which a target’s political economy evolves under mode-dependent rules. We analyze two modes: a permissive mode, in which a mechanism transmits pressure toward the sender’s preferred policy, and a contested mode, entered naturally once the target detects and attributes the mechanism. Crucially, the sender’s mechanism design shapes the transition into the contested mode rather than paying a static toll for legibility. This inverts the usual regime-switching problem: rather than estimating a latent transition kernel from data, the designer engineers the kernel to steer regime occupancy over a planning horizon. A structured switch vector decomposes any mechanism along discrete design dimensions, and a combinatorial optimizer searches this space for high-performing archetypes scored on compliance, time-to-threshold, and a durability ratio. We characterize mode-conditional equilibria and derive comparative statics on credibility and legibility, showing that the legibility penalty is scaled by the salience of the government channel and therefore interacts with the mechanism’s cost incidence. We illustrate the framework with two stylized mechanisms, report a proof-of-concept simulation over a reduced switch space, and report a small blind-audit study of the pipeline’s optional language-model generation stage. 22footnotetext: FUNDING: Research was sponsored by the Army Research Office and was accomplished under Cooperative Agreement Number W911NF-25-2-0040. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. Key words: geoeconomic influence; mechanism design; switching dynamical systems; hybrid systems; economic statecraft; decision analysis for policy design 1 Introduction Nations increasingly pursue geopolitical objectives through economic means. Trade policy (25), investment screening (4), technical standards (29), and financial infrastructure (11) have become instruments of statecraft deployed not to produce economic outcomes in isolation but to engineer the incentive environments of target states. The resulting literature on geoeconomic influence has produced important taxonomic and structural insights (2; 7; 11). However, it has largely treated the target nation as a unitary actor that responds to external pressure as a single strategic entity. This abstraction obscures the internal transmission structure through which influence actually operates. That structure provides the pathways by which external mechanisms route pressure through a target’s civil society, private sector, and government factions to produce a policy outcome. This paper develops a formal framework for analyzing indirect geoeconomic influence (IGI), in which a state (the sender) seeks a policy outcome in a target nation not by mandating it directly, but by engineering the target’s internal political economy so that its own citizens, firms, and institutions generate the compliance pressure. The framework decomposes influence mechanisms along discrete structural dimensions — choices about how pressure is timed, routed, and sustained within the target — and a combinatorial optimizer searches this space to identify high-scoring mechanism configurations. It operates generatively rather than inferentially, meaning it is designed to discover and evaluate novel mechanisms before deployment, not to recover behavioral patterns from historical data. The framework’s central modeling assumption is that a target’s political economy under influence does not evolve under a single set of rules. It switches. Before a mechanism is detected and attributed, the target’s government channel transmits externally originated pressure much as its private and civil-society channels do; the sender’s investment loads momentum that moves policy toward the sender’s preferred outcome. Once the target’s government identifies the mechanism, the same channel reverses: the government becomes a net source of counter-pressure, and its resistance capacity rises as it mobilizes. These are qualitatively distinct dynamical regimes, and the boundary between them is not exogenous. It is a function of the mechanism’s design — its legibility, external support, and cost incidence, among other design choices — together with the starting conditions. Modeling this boundary, and handling the sender design choices over it, is the analytical core of our paper. This orientation inverts the standard use of switching dynamical systems. In the tradition initiated by 13, one observes a time series generated by a system that operates under distinct regimes and estimates, after the fact, both the latent regime sequence and the transition kernel governing it. The IGI framework runs this machinery backward. The transition kernel is not estimated from data but designed: the sender’s switch vector shapes when the target enters a resistant regime and the policy problem becomes one of steering regime occupancy. Our approach facilitates, for example, maximizing time spent accumulating compliance in the permissive mode before the contested mode engages. Regime change is the object of design, not of inference. To our knowledge this reorientation is novel in the geoeconomic setting, and it is what makes the “switching” in switching dynamical system a technical commitment rather than a metaphor. The framework is developed for the interstate case but its logic extends to any setting in which an actor induces behavioral change in a complex system through indirect incentive design. Inducing private-sector firms to internalize national-security considerations in sourcing decisions without direct mandates is structurally identical: an actor engineers an incentive environment, pressure routes through internal subsystems, and a policy outcome emerges endogenously. Supply-chain resilience, conditional development finance, and multilateral coordination all fall within scope. The framework is positioned as a decision-analytic tool for designing policy interventions where randomized evidence is unavailable and outcomes depend on an adversary’s endogenous response. We argue this problem fits squarely within the concerns of structured decision analysis and adversarial risk analysis (23). Its intended use is prescriptive: to enumerate, compare, and stress-test candidate policy responses before deployment, producing policy-interpretable outputs suitable for simulation and wargaming. 2 Related Work The study of geoeconomic influence draws on several distinct literatures (21). Although no single one provides the formal dynamic framework this paper develops, each contributes theoretical grounding. We situate our contribution within four threads: economic statecraft, the formal modeling of sanctions and coercion, regime-switching and hybrid dynamical systems, and mechanism design. 2.1 Economic Statecraft 2 provides the foundational vocabulary and evaluative framework for the field. 1 traces how that vocabulary has been stretched by contemporary practice, as statecraft has moved from discrete instruments toward the reshaping of trade and technology regimes themselves. A central component is methodological: Baldwin argues that the effectiveness of economic instruments should be assessed comparatively, against a counterfactual, rather than against an absolute standard of full compliance. We adopt his basic framing of influence as an attempt by a sender to alter a target’s behavior through economic means, and his insistence that instrument choice be evaluated on cost-effectiveness grounds. Baldwin’s framework does not, however, provide a formal dynamic model of how instruments produce compliance, and his taxonomy is organized by instrument type (sanctions, aid, trade policy) rather than by the structural dimensions of how influence propagates through a target’s internal political economy. We propose a complementary decomposition at a finer level of structural resolution. 11 offer a theoretically developed contribution in which states and their relationships are modeled as a network. They argue that asymmetric network structures concentrate coercive power in hub nodes, and that states with jurisdiction over those hubs can weaponize interdependence through the panopticon effect (hub control generates surveillance advantages) and the chokepoint effect (hub control enables denial of access). Their framework is structural and external: it explains why hub states possess leverage but treats the target’s response as a function of network position rather than internal political dynamics. The transmission structure through which external pressure routes through a target’s subsystems toward a policy outcome is not theorized. This paper picks up where they leave off, proposing a formal model of that internal transmission structure, and, critically, of how it changes once the target reacts. 5 offer a practitioner-oriented survey of geoeconomic tools and argue that the United States has underutilized them relative to rising powers. Their taxonomy of instrument categories is descriptively useful for decomposing the structural dimensions of influence propagation, but does not provide a formal theoretical account. 2.2 Formal Modeling of Sanctions and Coercion 7 provides a rigorous game-theoretic treatment of economic sanctions. His conflict-expectations model explains why sanctions are imposed frequently despite a poor track record, by showing that adversarial relationships generate incentives to sanction that are independent of the probability of success. As Drezner states, the model rests on the assumption that governments act as rational unitary actors. This abstraction forecloses analysis of the internal transmission structure through which external pressure reaches a policy outcome: Drezner’s model has no civil society, no private sector, and no government factions. The IGI framework relaxes this assumption as its central move, decomposing the target into interacting subsystems whose differential response to external mechanisms determines the outcome. 15 represent the most direct attempt to open the target’s internal political economy to formal analysis. Working in the public-choice tradition, they model interest groups within the target as political demanders and suppliers of policy, and ask how external sanctions affect the equilibrium among them. They offer an insight that anticipates the core of our model: the political effects of sanctions depend on how economic pressure distributes across domestic constituencies. The critical difference is temporal, as their apparatus is static. It characterizes a political equilibrium and performs comparative statics on that set point. It has no time dimension, no accumulation of durable capital, no mechanism momentum, and no notion that the target’s response rules change once it reacts. The IGI framework extends their intuition into a dynamic, mode-switching setting in which the routing and persistence of pressure plus the timing of the target’s reaction determine the outcome. More recently, 18 demonstrate empirically that sanctions alter the bargaining environment between target governments and domestic civil-society campaigns, documenting the civil-society transmission channel the pressure vector formalizes, though they do not model the dynamics of that transmission. 8 documents a parallel private-sector channel in which targeted financial measures operate less through direct state compliance than through the risk calculations of banks and intermediaries. 26 identified a distinction that anticipates the IGI framework’s central theoretical move. Analyzing variation in the effectiveness of U.S. pressure on Japanese trade policy, he argues that direct strategies systematically underperform relative to synergistic strategies that deliberately activate and amplify domestic reform coalitions within the target. His concept of reverberation in which a sender’s demands strengthen the hand of domestic reformers is a qualitative description of the indirect-influence logic this paper formalizes. Schoppa’s work is foundational to the present effort. However, its typology is qualitatively inferred from case comparison rather than a formal dynamic model; it is specific to bilateral trade negotiations; and it is taxonomic rather than generative, classifying observed strategies without providing a method for discovering novel ones. 2.3 Regime-Switching and Hybrid Dynamical Systems 13 establishes the methodological foundation on which this paper builds. His insight is that a single set of dynamic equations is insufficient to describe a macroeconomic system that behaves under qualitatively different rules at different times. For example, gross domestic product dynamics switch between an expansion regime and a recession regime. The key contribution for our purposes is not the specific Markov-switching apparatus but the underlying philosophy: some systems are better characterized as operating under distinct behavioral regimes than as following a single continuous dynamic. Political economies under geoeconomic pressure exhibit exactly this structure, switching between permissive and contested regimes as a mechanism is detected. 16 develops the filtering machinery for this class, approximating the regime-conditional state distribution by collapsing it into a mixture weighted by regime probabilities. Our expected-trajectory formulation (Section 4.4) performs the analogous collapse in the generative direction: mode occupancy is propagated forward as a probability and the dynamics blended accordingly, rather than inferred backward from data. 12 demonstrate that switching state-space models are productive analytical tools well outside economics, applying variational inference to switching dynamics. When the mode boundary is driven by an accumulating state, the object is a hybrid dynamical system in the sense of 28: continuous dynamics within modes, transitions governed by that state. The proof-of-concept in this paper tracks the expected trajectory under an exposure-driven detection hazard, and notes the deterministic-guard and full-stochastic variants as extensions. A critical difference between this literature and the present paper deserves emphasis. 13 and 12 work in the inferential direction: they fit switching models to observed data to recover latent regimes and estimate transition probabilities after the fact. This paper works in the opposite direction. A vector of design choices is specified ex ante by a policy designer who enumerates, compares, and simulates mechanism configurations before deployment, and those choices shape the transition structure itself. The IGI framework is generative rather than inferential, prescriptive rather than descriptive. This reorientation from using an SDS to explain observed dynamics to using it to design desired ones is, to our knowledge, novel in the geoeconomic context. 2.4 Mechanism Design The indirect-influence framing shares the philosophical orientation of the mechanism-design tradition originating with 14: rather than mandating outcomes directly, the designer engineers the incentive environment such that the target’s own actors generate the desired outcome as an equilibrium. The IGI framework does not operate in the formal mechanism-design tradition (we do not specify complete games with typed agents, strategy spaces, and implementation theorems n the sense of 19) but the animating intuition is the same. Country A does not set Country B’s policy; it restructures B’s incentive environment so that B’s own citizens, firms, and institutions generate the compliance pressure. A second departure is computational. Where classical mechanism design asks what outcomes are implementable in principle, the algorithmic tradition (22) asks what a designer can actually compute. The IGI framework sits on that side, trading the generality of a full implementation result for an enumerable design space a policy analyst can search exhaustively. 3 The IGI Framework We model geoeconomic influence as an indirect engineering problem. Country A (the sender) seeks a policy outcome in Country B (the target) but does not directly set B’s policy. Instead, A deploys a mechanism that loads momentum into B’s system through targeted behavioral channels. This momentum routes through B’s internal subsystems (government, civil society, and the private sector) and resolves against B’s institutional resistance capacity. The policy outcome is endogenous to B’s own dynamics, not imposed from outside, and B’s dynamics are not fixed: once B detects and attributes the mechanism, its government channel switches from conduit to resistor. 3.1 Overview of the Pipeline Switch Vector Structural dimensions of mechanism design Optimizer Search over switch combinations Ranked Archetypes Optimized abstract mechanism configurations Model Scoring Cost-effectiveness and durability ranking LLM Generation Concrete mechanism instantiation Concrete Mechanisms Instruments with formal parameterization Playbook Actionable mechanism library optional Figure 1: The IGI framework pipeline. Dark boxes are primary inputs and outputs; light boxes are intermediate processing stages; dashed boxes are optional. The pipeline transforms a structured switch vector through combinatorial optimization into scored, actionable mechanism archetypes. An optional language-model generation stage translates archetypes into concrete candidate policy instruments; we report a proof-of-concept run of that stage in Section 8.6. The pipeline (Figure 1) operates as follows. Any influence mechanism is decomposed into structural dimensions, represented as a switch vector s. A combinatorial optimizer searches the Cartesian product of switch values for archetypes, or optimized abstract mechanisms, that maximize predicted compliance under the model of Section 4. High-scoring archetypes are scored on cost-effectiveness metrics (Section 5) and, optionally, translated by a language-model generation stage into candidate policy-instrument descriptions for further evaluation, wargaming, or simulation. 3.2 The Switch Vector Definition 1 (Switch Vector). A switch vector =(s1,…,sd)s=(s_1,…,s_d) is a d-dimensional vector in which each component sis_i takes a value from a finite candidate set iS_i. The Cartesian product =∏i=1diS= _i=1^dS_i defines the mechanism space: the set of all abstract mechanism configurations under the assumed decomposition. Table 1 presents eleven notional dimensions that illustrate an architectural decomposition of geoeconomic mechanisms. The dimensions are drawn from a review of geoeconomic instruments but are not definitive; they are a starting point for collaborative refinement rather than a finalized ontology. Not all switches are active in every mechanism: contingent switches may take null values and drop from the model; structural switches (e.g., locus of pressure) are always active. Two dimensions require explicit disambiguation because they are easily conflated. Locus of pressure identifies which of B’s internal subsystems (government, private sector, civil society, mixed) bears the primary pressure; it is the routing choice, and it is what the model’s pressure vector (Section 4.2) is defined over. Target population identifies which stratum of B’s society the mechanism addresses (elite, mass, institutional, networked). It conditions how readily pressure originating at that stratum reaches the routed subsystem, but it does not itself determine routing. A mechanism may, for example, address a networked professional population while routing pressure through the private sector. Table 1: Notional Mechanism Switch Vector Switch Candidate Values Influence timing Latent / Active / Mixed Target population Elite / Mass / Institutional / Networked Propagation pathway Direct / Cascade / Systemic Behavioral channel Divestment / Alignment / Mobility / Consumption Credibility mechanism Legal / Institutional / Market / Demonstrated Threat structure Automatic / Discretionary / Graduated Momentum persistence Low / Medium / High Feedback polarity Stabilizing / Destabilizing / Neutral Locus of pressure Government / Private sector / Civil society / Mixed Cost bearer Country A / Country B / Shared Legibility to B Transparent / Obscured / Deniable Note. Each row defines one candidate dimension of the switch vector s. The optimizer searches over combinations of these values to identify high-scoring archetypes. These dimensions are notional. 3.3 Optimization over Mechanism Space For a given geopolitical objective, an optimizer searches S for switch vectors that maximize a compliance objective (defined in Section 4.6). The discrete, enumerable structure of S means that for small switch spaces exhaustive search is feasible; for larger spaces, gradient-free methods (genetic algorithms, Bayesian optimization) trade coverage for speed. The proof-of-concept in Section 7 uses exhaustive enumeration over a reduced space. High-scoring archetypes serve as abstract blueprints that specify how influence is structured, routed, and sustained, without yet specifying a concrete policy instrument. An interpretation stage, by policy experts or via a language-model generation process, then contextualizes each archetype into candidate instrument descriptions reflecting the institutional specifics of the target. 4 Formal Model The formal model is a minimal switching dynamical system designed to distinguish mechanisms along the dimensions of the switch vector. It rests on three continuous state variables, a discrete mode variable, a pressure vector representing B’s internal political economy, and a set of switch-dependent functional parameters. The defining feature relative to the sanctions-modeling literature is that B’s response rules are mode-dependent, and the mode transition is endogenous to and shaped by A’s mechanism design. 4.1 State Space and Modes Three continuous state variables characterize the system at each period t: • yt∈[0,1]y_t∈[0,1]: Country B’s policy position, where 00 is full resistance to A’s preferred outcome and 11 is full compliance. • kt∈ℝ≥0k_t _≥ 0: structural entrenchment stock — accumulated leverage that persists independently of A’s ongoing investment (installed standards, certified exporters, asset positions held by B’s population). • mt∈ℝ≥0m_t _≥ 0: mechanism momentum — the mechanism’s current activation level, which may persist after A reduces investment (high momentum) or decay rapidly (low momentum). The system additionally carries a discrete mode zt∈P,Cz_t∈\P,C\: the permissive mode (PP), in which the mechanism operates before the target has detected and attributed it, and the contested mode (CC), in which the target’s government has identified the mechanism and mobilized against it. The mode governs which rules the continuous states obey (Section 4.3), and the transition P→CP is driven by an accumulating exposure stock Et∈ℝ≥0E_t _≥ 0 (Section 4.4). A’s mechanism is activated through a non-negative action variable at≥0a_t≥ 0 representing investment intensity at time t, with total investment bounded by budget C¯ C: ∑tat≤C¯ _ta_t≤ C. For interpretive purposes, yty_t admits a categorical overlay: [0,0.2)[0,0.2) active resistance; [0.2,0.5)[0.2,0.5) passive non-compliance; [0.5,0.8)[0.5,0.8) partial compliance; [0.8,1.0][0.8,1.0] full compliance. These bands are labels on the continuous state, not additional modes; the switching structure of the model lives in ztz_t, not in the y-bands. 4.2 Internal Pressure Vector Rather than treating B as a unitary actor, the model distinguishes three internal subsystems whose behavior transmits A’s mechanism to B’s policy outcome: • ptGp_t^G: pressure from or within B’s government, including internal faction dynamics and resistance capacity. • ptPp_t^P: pressure from B’s population and civil society. • ptFp_t^F: pressure from B’s private sector and firms. These form the vector t=(ptG,ptP,ptF)⊤p_t=(p_t^G,p_t^P,p_t^F) . The routing vector (,zt)=(λG,λP,λF)⊤∈ℝ3 (s,z_t)=(λ^G,λ^P,λ^F) ^3 distributes scalar mechanism momentum across the three pressure channels. Components may be negative. The routing depends on the mode: the government channel that transmits pressure in the permissive mode reverses sign in the contested mode.11 1 We treat as a vector rather than a matrix because momentum mtm_t is scalar in the present specification; a richer model with a vector-valued momentum state would promote to a matrix without altering the interpretation. The locus of pressure switch (Table 1) selects how a mechanism’s momentum is distributed across these three channels. Note that the fourth value, mixed, distributes pressure across the three internal subsystems. The pressure vector has three components; the four-valued switch determines their relative loading, not their number. In general, this demonstrates how pressure vectors can function as discrete or relative instruments. 4.3 Mode-Dependent Dynamics Within a given mode, the three continuous states evolve according to yt+1 y_t+1 =χyt+()⊤t−β(zt)r(yt,kt), =χ\,y_t+w(s) p_t-β(z_t)\,r(y_t,k_t), (1) kt+1 k_t+1 =kt+μ()at−κkt, =k_t+μ(s)\,a_t-κ\,k_t, (2) mt+1 m_t+1 =ρ()mt+ν()kt+η()at, =ρ(s)\,m_t+ν(s)\,k_t+η(s)\,a_t, (3) with yt+1y_t+1 clamped to [0,1][0,1] each period. Here χ∈(0,1]χ∈(0,1] is the policy-position inertia: the fraction of the current policy position carried into the next period. The baseline analytic treatment sets χ=1χ=1, so that policy position is a pure accumulator and (1) reduces to an increment on yty_t; the simulation retains χ as a free parameter (Section 7).22 2 We use χ rather than λ for this parameter to avoid collision with the routing components λG,λP,λFλ^G,λ^P,λ^F of Section 4.2. The weight vector ()=(wG,wP,wF)⊤w(s)=(w^G,w^P,w^F) gives the salience of each subsystem for the policy outcome. Its dependence on s is a modeling assumption: the salience is taken to follow the cost bearer switch, so that when A bears the mechanism’s cost weight concentrates on the government channel (wGw^G large), when B bears it weight shifts toward B’s own firms and population (wGw^G small), and shared cost weights the channels evenly. This encodes the intuition that whoever funds a mechanism shapes which of B’s subsystems it most directly loads; like the other switch-to-parameter mappings, it is an object of calibration rather than a derived quantity. In (1) the resistance term r(yt,kt)r(y_t,k_t) satisfies ∂r/∂yt>0∂ r/∂ y_t>0 (resistance rises with compliance) and ∂r/∂kt<0∂ r/∂ k_t<0 (entrenchment erodes resistance). The scalar β(zt)>0β(z_t)>0 is B’s baseline resistance capacity, and it is mode-dependent: β(C)≥β(P)β(C)≥β(P), reflecting that a government that has attributed the mechanism mobilizes resistance capacity it was not previously expending. In (2) structural stock accumulates with A’s investment at rate μ()>0μ(s)>0 and decays at rate κ>0κ>0. In (3) momentum persists at rate ρ()∈[0,1)ρ(s)∈[0,1), is fed by structural stock at rate ν()ν(s), and receives direct injection from A’s action at rate η()η(s). The pressure vector is t=(,zt)mtδ,p_t= (s,z_t)\,m_t\,δ, (4) where δ∈[0,1]δ∈[0,1] is A’s credibility as perceived by B’s internal actors. The routing vector is constructed in two steps. A base routing 0() _0(s) is determined by the locus-of-pressure switch; then a legibility adjustment is applied to the government component: λG(,zt)=λ0G()+g(ℓ()),zt=P,λ0G()−γ,zt=C,λ^G(s,z_t)= cases _0^G(s)+g ( (s) ),&z_t=P,\\[4.0pt] _0^G(s)-γ,&z_t=C, cases (5) where ℓ() (s) is the legibility switch value, ordered Deniable≺Obscured≺TransparentDeniable ; g(⋅)≤0g(·)≤ 0 is a non-positive legibility modifier, non-increasing in that order (more transparent mechanisms provoke more government resistance even before full attribution); and γ>0γ>0 is the sign-reversing penalty that engages when the target enters the contested mode. The population and private-sector components λP,λFλ^P,λ^F are mode-invariant in the baseline specification.33 3 Encoding legibility in the routing structure, rather than as a scalar attenuation applied uniformly to all pressure, is the more structurally meaningful choice: transparency activates targeted government counter-pressure rather than uniformly damping every channel, and locating it in the routing avoids double-counting against the exposure dynamics of Section 4.4. It also yields the sharper comparative static of Proposition 2. Equation (5) makes precise the sense in which the model switches. In the permissive mode the government channel transmits or mildly resists, if the mechanism is legible. In the contested mode, it reverses. The magnitude of the swing, and how close a permissive-mode mechanism already sits to the sign boundary, are both design choices encoded in s. Remark 1 (Functional forms). The specific forms of r(yt,kt)r(y_t,k_t), the switch-to-parameter mappings μ,ρ,ν,η,0,μ,ρ,ν,η, _0,w, the legibility modifier g(⋅)g(·), the contested-mode penalty γ, and the resistance ratio β(C)/β(P)β(C)/β(P) are not fixed by the framework. They are objects of empirical calibration. The proof-of-concept (Section 7) adopts the illustrative form r(yt,kt)=yt/(1+αkt)r(y_t,k_t)=y_t/(1+α k_t) and notional lookup-table values solely to demonstrate tractability. These choices are not claims about the true functional forms; the equations originate in a conceptual proposal and are deliberately provisional. 4.4 Endogenous Mode Switching The transition from permissive to contested is the analytical core of the framework and the locus of the sender’s design leverage. B accumulates an exposure stock driven by mechanism activity and scaled by legibility: Et+1=Et+ϕ(ℓ())(mt+ωat),E_t+1=E_t+φ ( (s) )\, (m_t+ω\,a_t ), (6) where ϕ(ℓ)≥0φ( )≥ 0 is increasing in legibility (transparent mechanisms are detected faster; deniable ones accrue exposure slowly), and ω≥0ω≥ 0 weights the visibility of direct investment relative to ambient momentum. Exposure drives a detection hazard: the per-period probability that B attributes the mechanism and transitions to the contested mode is ht= 1−exp(−Et/τ),h_t\;=\;1- \! (-E_t/τ ), (7) where τ>0τ>0 is a detection scale (larger τ means slower detection). Writing πt _t for the probability that the system has entered the contested mode by period t, πt _t evolves as πt+1=πt+(1−πt)ht _t+1= _t+(1- _t)\,h_t and is monotone non-decreasing, since the transition is irreversible. The reported trajectories are the resulting expected trajectories: the effective routing and resistance at each period interpolate between the permissive and contested regimes in proportion to πt _t, Φteff=(1−πt)Φ(,P)+πtΦ(,C),βteff=(1−πt)β(P)+πtβ(C). ^eff_t=(1- _t)\, (s,P)+ _t\, (s,C), β^eff_t=(1- _t)\,β(P)+ _t\,β(C). (8) This expected-trajectory formulation is the deterministic reduction of a stochastic detection process; it keeps the simulation cheap while letting dwell time vary smoothly with legibility. We report the period at which πt _t first crosses 0.50.5 as the mechanism’s dwell time. Two properties of (6)–(7) deserve emphasis. First, EtE_t is non-decreasing and, for any mechanism with ϕ(ℓ)>0φ( )>0 under sustained investment, unbounded; the detection hazard hth_t therefore approaches 11 and the contested-mode probability πt→1 _t→ 1; detection is not something a design can avoid, only defer. The design question is when, not whether. Second, because ϕφ depends on legibility and the drivers of EtE_t include both momentum and investment intensity, the mechanism designer directly shapes the dwell time in the permissive mode. This is the design lever the framework is built around: aggressive, high-visibility funding accumulates compliance quickly but also raises the contested-mode probability faster; a deniable, slow-loading mechanism buys a longer permissive window at the cost of slower accumulation. Remark 2 (Expected trajectory, deterministic guard, and full hazard). The model reports the expected trajectory under the detection hazard (7): mode occupancy is tracked by the probability πt _t and the dynamics are blended via (8), which is deterministic to compute and yields smooth dependence of dwell time on legibility. Two variants bound this choice. Setting the transition to fire the first time EtE_t crosses a threshold recovers a deterministic guard — a hybrid system with a single switching surface (28) — while sampling the transition time from the hazard and averaging over realizations gives the full stochastic form, closer to the Markov-switching lineage of 13. The expected-trajectory reduction used here approximates the mean of the stochastic form and avoids Monte-Carlo simulation over switching times; we note the two variants as extensions. 4.5 Within-Mode Equilibrium Because the mode switches at most once and irreversibly, the system admits a clean two-phase analysis: a within-mode fixed point exists for each mode, and the trajectory is a permissive-mode transient toward (yP∗,k∗,m∗)(y^*_P,k^*,m^*) that, once the contested mode engages, is redirected toward the contested-mode fixed point (yC∗,k∗,m∗)(y^*_C,k^*,m^*). Throughout this subsection we take investment to be constant at at=a∗a_t=a^*, as in the uniform-investment specification of Section 4.6. Setting Δy=Δk=Δm=0 y= k= m=0 within a mode, and noting that (2)–(3) are mode-invariant, the stock and momentum fixed points are pinned by a∗a^*: k∗ k^* =μ()a∗κ, = μ(s)\,a^*κ, (9) m∗ m^* =(ν()μ()/κ+η())a∗1−ρ(), = (ν(s)\,μ(s)/κ+η(s) )\,a^*1-ρ(s), (10) with ρ()<1ρ(s)<1 required for m∗m^* finite. Define the mode-dependent effective pressure scalar Φ(,z)=()⊤(,z). (s,z)\;=\;w(s) (s,z). (11) With χ=1χ=1, the within-mode equilibrium policy position satisfies Φ(,z)m∗δ=β(z)r(yz∗,k∗). (s,z)\,m^*\,δ\;=\;β(z)\,r(y^*_z,k^*). (12) With r(y,k)=y/(1+αk)r(y,k)=y/(1+α k), (12) solves in closed form within each mode: yz∗=clip[0,1](Φ(,z)m∗δ(1+αk∗)β(z)).y^*_z\;=\;clip_[0,1]\! ( (s,z)\,m^*\,δ\,(1+α k^*)β(z) ). (13) The clip reflects the y∈[0,1]y∈[0,1] constraint and binds at both ends: sufficiently high-influence combinations would saturate at full compliance in the permissive mode, and mechanisms whose government-channel reversal drives Φ(,C) (s,C) negative are floored at zero in the contested mode. Where either bound binds, it must be accounted for when interpreting rankings. For χ<1χ<1 the stationarity condition is (1−χ)yz∗=Φ(,z)m∗δ−β(z)r(yz∗,k∗)(1-χ)\,y^*_z= (s,z)\,m^*\,δ-β(z)\,r(y^*_z,k^*), and (13) generalizes to yz∗=clip[0,1](Φ(,z)m∗δ/[(1−χ)+β(z)/(1+αk∗)])y^*_z=clip_[0,1]\! ( (s,z)\,m^*\,δ/[\,(1-χ)+β(z)/(1+α k^*)\,] ), recovering (13) as χ→1χ→ 1; the comparative statics below are unaffected in sign. Equation (12) supports comparative statics. Because Φ and β are mode-dependent, each statement below is a within-mode claim; the framework’s substantive predictions concern how the permissive-mode transient and the contested-mode fixed point compare, and how long the system dwells in each. Proposition 1 (Credibility). Within either mode, and for Φ(,z)>0 (s,z)>0, equilibrium compliance yz∗y^*_z is weakly increasing in A’s credibility δ. Proof sketch. The left-hand side of (12) is linear and increasing in δ when Φ>0 >0; with ∂r/∂y>0∂ r/∂ y>0, the fixed-point condition forces yz∗y^*_z upward to restore balance. Uniqueness follows from monotonicity of r in y given the sign restrictions of Section 4.3. The claim is weak rather than strict because of the clip in (13). When Φ(,z)<0 (s,z)<0, as may obtain in the contested mode, the direction reverses: credibility amplifies counter-pressure. ∎ Proposition 2 (Legibility and cost incidence). In the permissive mode, equilibrium compliance yP∗y^*_P is weakly decreasing in legibility (under the ordering of Section 4.3), and the size of the legibility penalty is proportional to the salience wG()w^G(s) of the government channel. Consequently, mechanisms whose costs fall on B (small wGw^G) are partially insulated from the legibility penalty; in the limiting case wG=0w^G=0, legibility does not affect yP∗y^*_P. Proof sketch. A more legible mechanism lowers λGλ^G via the non-positive modifier g(⋅)g(·) in (5). Its effect on the effective pressure scalar is ∂Φ/∂λG=wG∂ /∂λ^G=w^G from (11), so the reduction in Φ is wG|Δg|w^G\,| g| for a one-step increase in legibility. Substituting into (12) and using ∂r/∂y>0∂ r/∂ y>0 gives the monotonicity claim, with magnitude scaled by wGw^G. When wG=0w^G=0 the government channel carries no weight and legibility drops out of (11) entirely. ∎ Remark 3 (A falsifiable structural claim). Proposition 2 is not merely a technical observation. It asserts that the cost of being seen depends on who bears the mechanism’s cost—a claim that could in principle be confronted with evidence on how detection affects mechanisms of differing cost incidence. That the wG=0w^G=0 case makes legibility costless is a sharp, testable prediction of the routing encoding rather than an artifact. Proposition 3 (Dwell time and durability). Fix the permissive-mode effective pressure Φ(,P) (s,P). Then cumulative compliance is increasing in permissive-mode dwell time, which is in turn decreasing in legibility ℓ() (s) and in investment visibility ω. For mechanisms with ρ()→1ρ(s)→ 1, compliance accumulated during the permissive window persists into the contested mode, so durability is governed jointly by dwell time and momentum persistence. Proof sketch. From (6)–(7), the exposure stock rises more slowly when ϕ(ℓ)φ( ) is small (deniable) and when the drivers mt+ωatm_t+ω a_t are small, so the detection hazard stays low longer; thus dwell time falls in legibility and in investment visibility. Compliance accrues in the permissive mode at a rate set by Φ(,P) (s,P); holding that rate fixed, a longer window integrates more compliance before the contested mode engages. As ρ→1ρ→ 1, momentum, and hence pressure, decays slowly after the transition, so permissive-mode gains are retained. The conditioning on Φ(,P) (s,P) is essential: dwell time is not valuable in itself, and a mechanism that loads no pressure gains nothing from a long permissive window. A full statement requires the within-mode transient, given in closed form for the PoC specification. ∎ Propositions 1–3 together express the framework’s central tension: aggressive designs accumulate compliance quickly but raise the detection hazard sooner, while deniable, slow-loading designs preserve the permissive window. This trade-off is what generates a non-trivial cost-effectiveness frontier and what makes mechanism selection genuinely scenario-dependent. 4.6 Optimization Problem Given a mechanism design s and budget C¯ C, A selects an action path at\a_t\ to maximize cumulative compliance over the horizon: max∑t=0T,atyts.t.∑t=0Tat≤C¯,at≥0, _s,\,\a_t\\; _t=0^Ty_t .t. _t=0^Ta_t≤ C, a_t≥ 0, (14) where the trajectory yt\y_t\ is generated by the mode-switching dynamics (1)–(7). The objective integrates compliance across both modes; because the action path affects both the rate of compliance accumulation and the timing of the mode switch through (6), (14) is not separable across time in general. The proof-of-concept restricts attention to uniform investment at=C¯/Ta_t= C/T and optimizes over s only. Joint optimization over at\a_t\, in particular, front-loading versus spreading investment to manage exposure, is a natural extension. 5 Cost-Effectiveness Metrics The optimization structure supports cost-effectiveness comparison across mechanisms on a common footing. Three metrics follow from the model: • Compliance efficiency: cumulative compliance per unit of total investment, (∑tyt)/C¯ ( _ty_t )/ C. Because the proof-of-concept fixes total investment at C¯ C with uniform allocation, this is a constant rescaling of cumulative compliance; the two are not independent axes. • Time to threshold: the number of periods to reach a specified compliance level y¯ y, capturing how quickly a mechanism loads and, under the mode-switching dynamics, whether it reaches y¯ y before the contested mode engages. The metric is right-censored at T: mechanisms that never reach y¯ y within the horizon are recorded as censored rather than assigned a numerical time, and are excluded from comparisons on this metric. • Durability ratio: compliance maintained after A withdraws investment relative to peak compliance, operationalized in the PoC by zeroing investment at T/2T/2 and measuring residual compliance at T. It is governed jointly by ρ()ρ(s), k∗k^*, and whether the system has entered the contested mode. The durability ratio is particularly important for policy evaluation. Mechanisms with high upfront cost but high durability (e.g., standards entrenchment) may dominate lower-cost mechanisms requiring continuous investment over long horizons. The mode-switching structure sharpens this: a mechanism that accumulates durable compliance before detection can retain it after the government mobilizes, whereas one that relies on ongoing permissive-mode transmission collapses once the sign reverses. For applied use, mechanisms are displayed on a cost-effectiveness Pareto frontier over compliance efficiency and durability, allowing policymakers to compare instruments on cost-effectiveness and durability without engaging the underlying mathematics. 6 Mechanism Illustrations We illustrate the framework with two stylized mechanisms that differ sharply in their switch-vector configurations and consequent dynamics. These are analytic illustrations, not empirical case studies, of how the same formal structure generates qualitatively different predictions—and, in particular, how the mode-switching machinery distinguishes mechanisms that a single-mode model would rank identically. Each illustration below highlights the switch dimensions most salient to the mechanism rather than enumerating all of Table 1; dimensions left unstated take non-distinctive or default values and are omitted for readability. The proof-of-concept implementation (Section 7) operationalizes a six-dimension subset of the switch vector; accordingly, the switch tuples in Table 2 report those six coordinates. 6.1 Mechanism I: An Emigration Option Contract Example 1 (Emigration contract). Country A offers citizens of Country B a guaranteed immigration pathway valid for a defined window, at zero cost to exercise. No mass emigration need occur for the mechanism to exert influence. The switch vector is characterized as follows: influence timing latent-first (the unexercised option does the work); target population networked (the mobility-sensitive professional stratum); propagation pathway cascade (elite behavior shapes institutional preferences broadly); behavioral channel divestment plus alignment-seeking; momentum persistence low (the option expires); locus of pressure civil society (ptPp_t^P primary); cost bearer B (lost human capital); legibility obscured (appears as a standard immigration program). In the model this produces low μ()μ(s), moderate direct injection η()η(s), and low ρ()ρ(s), with pressure loading primarily on ptPp_t^P. The mode-switching structure gives this mechanism a distinctive profile. Because its cost falls on B, the government channel carries little of the mechanism’s weight (wGw^G small), so Proposition 2 implies it is relatively insulated from legibility penalties: the contested-mode reversal acts on a channel that barely enters its influence. Its latent option also loads momentum steadily through η, so compliance accumulates during the permissive window and its structural stock retains a modest fraction of that compliance after detection. 6.2 Mechanism I: A Conditional Liquidity Corridor Example 2 (Conditional liquidity corridor). Country A establishes credit facilities for B’s private banking sector whose cost varies continuously with B’s regulatory alignment, as measured by a published policy index. The switch vector differs sharply: momentum persistence low (the mechanism requires ongoing investment; if A withdraws the facility it collapses); locus of pressure shifts to ptFp_t^F (B’s firms bear the cost gradient and lobby government directly); behavioral channel alignment-seeking; legibility obscured (the index is public but the causal chain from index to credit cost to lobbying is not); cost bearer shared (A sustains the facility while B’s firms bear compliance costs). Structural stock ktk_t accumulates as B’s firms build compliance infrastructure, but since it accrues to B’s private sector rather than to A, A must sustain ata_t to maintain influence. The mode-switching machinery makes the contrast precise. Both mechanisms are obscured, so by (6) they share the same exposure rate ϕ(ℓ)φ( ); what differs is how fast each drives exposure. The emigration contract loads momentum through its latent option (higher η), so its exposure stock EtE_t accrues faster and it reaches the contested mode sooner (dwell 1313 versus 1515). Yet it still dominates: during its shorter permissive window it accumulates more compliance, and its structural stock retains more of that compliance after detection than the liquidity corridor, whose low persistence (ρ) lets permissive-mode gains decay once the government channel reverses. The two-phase model thus separates the mechanisms in a way a single-mode model cannot—not through a speed-versus-durability trade-off between them, but by showing that a faster-loading mechanism can be detected earlier and remain more effective throughout. The illustration is therefore one of dominance with an instructive mechanism, not of a frontier: neither budget horizon nor strategic patience reverses the ordering. The two mechanisms illustrate the model’s dynamics rather than a design frontier. Figure 2: Policy-position trajectories yty_t over the T=30T=30 horizon for the two illustrative mechanisms of Section 6 and the optimizer’s top-ranked archetype. Filled dots mark each mechanism’s dwell time: the period at which the contested-mode probability πt _t first crosses 0.50.5. Because πt _t rises continuously from the first period, the government-channel reversal is blended in gradually via (8) rather than arriving as a discrete event, and each trajectory turns over once rising resistance βteffr(yt,kt)β^eff_t\,r(y_t,k_t) overtakes the forcing term Φteffmtδ ^eff_t\,m_t\,δ. For the two low-persistence mechanisms this occurs several periods ahead of the dot; for the high-persistence archetype, whose momentum keeps the forcing term growing, it roughly coincides with it. The aftermaths then separate on persistence and cost incidence: the liquidity corridor decays to near zero; the emigration contract retains roughly half its peak, since its cost falls on B and the reversing government channel therefore carries little of its weight (wGw^G small, cf. Proposition 2); and the top archetype partially recovers as accumulated momentum reasserts pressure. The two illustrative mechanisms are hand-specified rather than optimizer selections. Under the illustrative lookup values of Section 7 the whole archetype space sits below the compliance ceiling; the vertical scale is set accordingly. Table 2: Illustrative Mechanisms Located in the PoC Switch Space Mechanism Switch vector (6-dim.) Cumul. compl. Durability Dwell Rank Emigration contract Latent / Civil society / Cascade / Low / Obscured / B 0.941 0.077 13 287 Liquidity corridor Active / Private sector / Direct / Low / Obscured / Shared 0.325 0.019 15 638 Note. The two mechanisms of Section 6 are hand-specified narrative archetypes, not optimizer selections; their neither near-optimal nor near-worst ranks (of 972972) reflect that they illustrate the framework’s expressiveness rather than maximize compliance. Both carry Low momentum persistence, so both shed most compliance after investment withdrawal (low durability), consistent with the Section 6 narrative. Dwell is permissive-mode dwell time in periods. Values are illustrative, from the uncalibrated mode-switching parameterization. Metrics are defined in Section 5. The switch vector is in the order influence timing / locus of pressure / propagation pathway / momentum persistence / legibility / cost bearer. 7 Proof-of-Concept Simulation To demonstrate the pipeline’s tractability, we implemented a reduced-form version of the framework as a local simulation tool. The proof-of-concept (PoC) uses a six-switch vector (influence timing, locus of pressure, propagation pathway, momentum persistence, legibility to B, cost bearer) with three to four candidate values per switch, yielding 35×4=9723^5× 4=972 enumerable combinations.44 4 Five ternary switches and one quaternary switch (locus of pressure). The synthetic testbed is domain-agnostic: it removes any real-world calibration burden so that the scientific claim concerns the pipeline’s properties, not the prediction of historical outcomes. Design. The PoC evaluates the mode-switching model of Section 4 through three studies that share one simulator and vary different inputs. Table 3 summarizes the design. Table 3: Proof-of-Concept: Three-Study Design Study What varies What is held fixed Scenario sweep Scenario parameters α,β,δ,κα,β,δ,κ, perturbed one at a time about baseline Lookup tables; initial conditions at baseline Lookup robustness Switch-to-parameter lookup values, perturbed within ordered tiers (100100 draws) Scenario parameters at selected configurations Initial-condition map Initial policy y0y_0 and entrenchment k0k_0 over a 7×77× 7 grid Scenario parameters and lookup tables at baseline Note. All three studies re-run the full optimizer (972972 combinations) at each grid point or draw. The scenario sweep is reported here in one-at-a-time form; a full 625625-cell factorial grid over the four scenario parameters is implemented and available in the accompanying code. Total wall-clock time for the three studies is approximately 1010 seconds using an AMD Ryzen AI 9 HX 370 machine running Windows 11. Illustrative functional forms. The simulation adopts r(yt,kt)=yt/(1+αkt)r(y_t,k_t)=y_t/(1+α k_t), which satisfies the sign restrictions of Section 4.3 and admits a clean within-mode closed form. It is chosen for tractability, not empirical grounding; the true form is an open question. Notional parameter mappings. The switch-to-parameter lookup tables assign numerical values to ρ,μ,η,ν,ρ,μ,η,ν,w, and 0 _0 from qualitative reasoning about the switch dimensions, together with the mode-switching quantities: the legibility modifier g(⋅)g(·) and exposure rate ϕ(⋅)φ(·), the contested-mode reversal γ, and the resistance ratio β(C)/β(P)β(C)/β(P). These values are illustrative—intended to demonstrate that the pipeline distinguishes mechanisms and produces a sensible ranking, not to represent calibrated estimates. Table 4: Baseline parameter values for the proof-of-concept. These are illustrative choices to demonstrate tractability, not calibrated estimates (Remark 1). Parameter Symbol Value Planning horizon T 3030 Budget C¯ C 1.01.0 Resistance curvature α 1.01.0 Baseline resistance (permissive) β(P)β(P) 0.50.5 Contested resistance ratio β(C)/β(P)β(C)/β(P) 2.02.0 Policy inertia χ 0.850.85 Credibility δ 0.80.8 Entrenchment decay κ 0.10.1 Detection scale τ 5.05.0 Investment visibility ω 1.01.0 Threshold (time-to-threshold) y¯ y 0.50.5 Results. The PoC computes, for each of the 972972 archetypes, equilibrium and cumulative compliance, time to threshold, durability ratio, and permissive-mode dwell time, and ranks archetypes accordingly. Its purpose is to establish that the inverted regime-switching model of Section 4 is computable end to end, not to draw substantive conclusions about which mechanisms are preferable. Two observations suffice to establish this. First, the mechanism space is differentiated: archetypes vary materially in their scored metrics rather than collapsing to a common value, so the scoring resolves distinctions among designs. The two quantities that exist only because the model switches modes both take a range of values across the space. The durability ratio takes 577577 distinct values spanning [0.000,0.477][0.000,0.477], and permissive-mode dwell time takes 2424 distinct values spanning 77 to 3030 periods, where the upper value coincides with the horizon T=30T=30 and denotes mechanisms not yet detected within it (right-censored, as with time to threshold). The mode-switching dynamics are therefore exercised rather than dormant. Moreover, a Pareto frontier over compliance efficiency and durability retains 99 of the 972972 archetypes, indicating that the two metrics are not redundant: the space contains genuine trade-offs rather than a single dominant design. Second, the pipeline responds to its inputs in a structured way. Varying scenario parameters, lookup values, and initial conditions produces systematic variation in the ranked output rather than noise, which is what the three sweeps of Table 3 demonstrate. We report these sweeps as evidence that the machinery is exercisable across its input space, not as findings about geoeconomic influence; their specific rankings are artifacts of an illustrative parameterization and carry no substantive weight. The PoC does not establish that any particular mechanism archetype is optimal, nor that the mechanism space partitions into interpretable regimes; whether such structure exists is a question for a calibrated model, not this demonstration. Regularities that do appear in the sweeps are analytic consequences of Propositions 1–3 rather than empirical discoveries, and we treat them as confirmation that the implementation is faithful to the model. The clearest instance is that the top-ranked cluster is constant on two dimensions, taking momentum persistence == High and cost bearer == B throughout. This is exactly what Propositions 2–3 predict—high persistence retains permissive-mode gains, and cost incidence on B lowers wGw^G and so insulates against the legibility penalty—and we report it as an implementation check, not a result. Implementation notes. Three properties of the demonstration should be read carefully. Under the illustrative lookup values the entire archetype space sits well below the compliance ceiling: the highest peak policy position of any of the 972972 archetypes is approximately 0.290.29, so the y∗=1y^*=1 clip in (13) never binds and every mechanism remains in a low-compliance regime. This reflects the provisional parameterization, not a property of the framework, and it does not affect the proof-of-concept’s claims, which are ordinal (differentiation, ranking, and the cost-effectiveness frontier) rather than statements about absolute compliance levels. Differentiation among archetypes accordingly rests on transient speed, dwell time, and durability. The lookup-robustness sweep perturbs values within ordered tiers, so it exercises the pipeline against magnitude variation but holds the ordinal structure of the qualitative assignments fixed; the ordinal assumptions themselves are a calibration question, not something the PoC probes. And the policy update (1) carries the inertia term χ, whose interaction with baseline resistance β must satisfy a mild stability condition for initial conditions to influence trajectories: writing the policy self-map at low entrenchment (r≈yr≈ y) as yt+1≈(χ−β)yt+(forcing)y_t+1≈(χ-β)\,y_t+(forcing), genuine and stable dependence on initial conditions requires 0<χ−β<10<χ-β<1. Below the lower bound the update suppresses the initial position rather than propagating it; above the upper bound it fails to contract. The baseline parameterization (χ=0.85χ=0.85, β=0.5β=0.5) gives χ−β=0.35χ-β=0.35. This is a property of the discrete update, noted here for reproducibility. Transition to empirical calibration. The PoC demonstrates that the pipeline architecture is computationally tractable and produces discriminating output under illustrative parameterization. Transition to a calibrated model requires: (i) empirical estimation or expert elicitation of the switch-to-parameter mappings, including the new mode-switching quantities (g,ϕ,γ,τg,φ,γ,τ, and the resistance ratio); (i) selection of functional forms for r, the mode-transition hazard, and the mapping functions, guided by case evidence; and (i) validation of predictions, especially dwell-time and durability predictions, against historical episodes of geoeconomic influence. 8 Discussion The framework’s contribution is to take seriously the internal transmission structure through which indirect influence operates, and to model the moment that structure changes — when the target detects the mechanism and its government channel reverses. We discuss scope, generalizability, the analytic-versus-emergent character of the results, and the framework’s ethical posture. 8.1 Scope Conditions We have positioned the IGI approach as a means of geopolitical influence. The same architecture may apply to the discovery of policies for internal deployment by a nation, a firm, or another large-scale organization, and possibly as a tool for designing policies in computer-science settings. As specified, however, it is best suited to target nations with meaningful internal political economies. Targets without sufficiently distinct and autonomous civil societies, private sectors, and government factions cannot route the pressure a mechanism creates. The empirical sanctions literature supports this boundary directly. 17 show that sanctions are systematically less effective against nondemocratic targets, arguing that the key to success is generating political costs for the regime’s winning coalition; in autocracies that coalition is small, rents accrue to insiders, and the internal transmission channels are weak or absent. The IGI framework formalizes this: in the limiting case where B’s civil society and private sector exert no independent influence, the pressure vector collapses toward the government subsystem, and, because that channel is precisely the one that reverses in the contested mode, external mechanisms lose their primary lever the moment they are detected. The unitary-actor assumption of the formal sanctions literature (7) is more than an abstraction; it is a reasonable approximation for a specific and important class of targets. The framework’s contribution is to make explicit when that approximation holds and when it breaks down. Case evidence is consistent: 24 document that targeted sanctions contributed to reform in Myanmar, where internal channels were sufficiently autonomous to transmit pressure, but failed in Zimbabwe, where the regime’s entrenchment blocked those channels. 8.2 Generalizability The underlying logic (engineering an incentive environment so that a target system’s own actors generate the desired pressure) extends beyond the interstate case. Two extensions are noteworthy. Domestic supply-chain resilience: inducing private-sector firms to internalize national-security considerations in sourcing without direct mandates is structurally identical to the foreign-policy case. The locus of pressure shifts to the private-sector subsystem, the behavioral channel becomes alignment-seeking, and the designer is a domestic government rather than a foreign state. The switch-vector approach accommodates this without structural modification, and the mode-switching structure applies too: firms and regulators “detecting” and resisting an incentive scheme is the same detection-triggered transition. Conditional development finance: IMF structural conditionality instantiates the liquidity-corridor mechanism. It is an external actor offering financial access whose terms vary with policy compliance, routing pressure through domestic financial institutions that lobby the government. The conditionality literature documents precisely the internal transmission dynamics the model predicts (20; 6). A third connection is historical: 27 documents that synergistic strategies — deliberately activating aligned domestic coalitions — deployed in U.S.–Japan trade negotiations had measurable effect, and that their success tracked the availability of those internal coalitions, consistent with the IGI framework’s pressure-routing predictions. 8.3 Analytic versus Emergent Results A methodological point deserves emphasis for readers evaluating the simulation. Some of the framework’s regularities are analytic: they follow directly from the equilibrium conditions and comparative statics of Section 4. That compliance rises with credibility (Proposition 1) and that deniable, high-persistence mechanisms score well in the permissive mode are corollaries of the model’s monotone structure, not discoveries of the simulation; a simulation that “found” them would merely be confirming the algebra, and we treat their appearance in the sweeps as a check that the implementation is faithful. Other questions are empirical and cannot be read off the equilibrium conditions, including which archetype is preferable as a function of initial conditions, and whether the permissive/contested trade-off makes selection depend on scenario rather than being dominated by a single archetype. The proof-of-concept does not answer these. Answering them requires a calibrated model, and under the illustrative parameterization no such selection structure should be inferred. What the distinction buys, even ahead of calibration, is a map of where simulation would be load-bearing (selection, dwell time, the frontier) versus redundant with theory (monotone comparative statics). 8.4 Sensitivity to Parameterization The ranking of archetypes depends on the switch-to-parameter mappings, which in the PoC are illustrative rather than calibrated (Remark 1). This sensitivity is a feature. Varying parameter values around baseline identifies which parameters most influence the ranking, and therefore which mappings most urgently require calibration. This is analogous to prior-sensitivity analysis in Bayesian models. The framework is designed to make this diagnostic transparent: as case evidence, natural experiments, or expert elicitation constrain the parameter space, the archetype rankings update without altering the model’s structure. Under the mode-switching model the same logic extends to the transition quantities: the detection threshold τ and exposure rate ϕφ are prime elicitation targets precisely because dwell time is where the interesting trade-offs live. 8.5 The Archetype-to-Instrument Gap The pipeline produces abstract archetypes, or structured descriptions of how influence is timed, routed, and sustained. It does not produce concrete instruments. Translating an archetype into an actionable instrument requires contextual judgment about the target’s institutions, culture, and political economy. The optional language-model generation stage (Figure 1) assists this translation but introduces a validity question: does the generated description faithfully reflect the archetype’s structural properties, including its mode-switching profile, or does it drift? Wargaming and structured expert review are the natural validation mechanisms. Participants can probe whether a candidate instrument would route pressure through the specified channels and whether its credibility, persistence, and, crucially, detectability properties survive contact with real institutional constraints. Full validation is beyond the present scope, but is a necessary condition for operational use; Section 8.6 reports a first, deliberately narrow step toward it. 8.6 Instantiating the Generation Stage: A Proof-of-Concept Run The pipeline (Figure 1) posits a final stage translating an abstract archetype into a concrete candidate instrument. We ran that stage once, as a proof of concept, on the three mechanisms of Section 6: the two hand-specified illustrations and the optimizer’s top-ranked archetype. The exercise is small—nine generations from a single prompt and a single model—and we report it as a demonstration that the stage runs and can be audited, not as a validated capability. Procedure. A fixed prompt (Appendix A) supplied only the six switch values and the synthetic Civilization A/B setting, and requested a concrete instrument as structured output. Three generations were produced per archetype. We then audited faithfulness two ways. In the self-report check, the generating model also stated which switch values its own instrument reflected. In the blind check, a second pass classified each narrative into a switch vector after the source archetype and the self-report had been stripped and the nine narratives shuffled; recovered vectors were then compared to the true archetypes. Both passes used Claude Sonnet 5 (22 July 2026), each run in a fresh incognito session so that no conversational history, memory, or personalization carried between generation and classification. Self-report is uninformative. Self-reported vectors matched the requested archetype on all 5454 dimensions (100%100\%). This result carries almost no evidential weight: because the generating model saw the archetype, a match is equally consistent with faithful instantiation and with copying the input back. We report it only to document that the obvious audit does not work, and that a blind procedure is necessary. The blind check is informative. Blind classification recovered 41/5441/54 switch dimensions (76%76\%; Table 5). Failures were systematic rather than scattered, and two of them were unanimous across all three generations of an archetype. They admit three distinct diagnoses. Generation drift. One instrument (top archetype, generation 3) made continued benefits explicitly conditional on B’s policy, a visible demand from A, which the blind pass read as Obscured/Mixed rather than the requested Deniable/Latent. Its recorded rationale identifies the departure precisely: years of dormant, unexercised protocol lock-in do the structural work, but A later issues an explicit active conditional signal to trigger the payoff. The instrument departed from its specification, the classification recovered the departure from the narrative alone, and the generator’s self-report did not register it. Systematic drift under joint constraint. All three liquidity-corridor instruments were classified Cascade rather than the requested Direct, and the classifier’s stated reasons track the text: each narrative turns on competitive spread between adopting firms and holdouts. One reading is that this switch value is difficult to instantiate jointly with the rest of the vector (an instrument in which the private sector pressures government without propagating among firms is hard to write), in which case the drift is informative about the mechanism space rather than about the model. Taxonomy ambiguity. Eight of the thirteen misses fell on two dimensions whose definitions did not survive contact with a classification task. Four fell on cost bearer, where the classifier’s rationales reason uniformly from who funds the instrument—A’s ministry subsidizing credit, A financing scholarships and intermediaries—while the archetypes assign the value by who absorbs the consequences. Table 1 conflates the two, and both readings are textually supported. The remaining four fell on legibility, where the difficulty is more instructive. Table 1 defines legibility by how readily B identifies and attributes a mechanism. That definition proved insufficient to resolve cases blind; the classification rubric therefore added an operational criterion absent from the taxonomy, that an explicit conditional demand from A counts against deniability (Appendix A.2). That criterion then drove the calls: instruments voicing no conditional demand were read as Deniable, including all three emigration instruments specified as Obscured. These misses are therefore partly an artifact of operationalization rather than evidence about the narratives. This is itself informative: a dimension that cannot be applied without inventing a criterion is a dimension that does not yet decide cases. Both dimensions require revision before elicitation. Table 5: Archetype-to-instrument round-trip recovery (blind pass) Archetype Gen. Blind match Dimensions not recovered Emigration contract 3 13/18 legibility (33), locus of pressure (11), cost bearer (11) Liquidity corridor 3 13/18 propagation (33), cost bearer (22) Top archetype 3 15/18 legibility (11), timing (11), cost bearer (11) Overall 9 41/54 (76%76\%) legibility (44), cost bearer (44), propagation (33), timing (11), locus of pressure (11) Note. A blind pass classified each generated narrative into a switch vector without access to the source archetype or the generator’s self-report. A recovered dimension indicates that the design choice is legible in the instrument description. Self-reported (non-blind) matches were 54/5454/54 and are not reported as evidence. Generated with Claude Sonnet 5; outputs are committed verbatim in the supplement. A useful control, and what does not follow. A narrative that explicitly described its own attributability, noting that sustained analysis would eventually trace financing back to A, had its legibility recovered correctly. This indicates that the blind pass distinguishes the value when the text marks it, and that the emigration failures reflect absent cues rather than indiscriminate classification. Several limits nonetheless bound what this run establishes. Running each pass in a separate incognito session precludes conversational or memory-based leakage, but both passes used the same model, so what is withheld is the information, not the model’s priors; genuine independence requires a different classifier, and inter-rater agreement cannot be estimated from a single pass. Nine generations from one prompt cannot separate prompt-specific from model-specific behavior. And the model is version-contingent: the prompt is fixed and published, but exact regeneration is not guaranteed, so the committed outputs rather than the procedure are the reproducible artifact. Interpretation. Read conservatively, the run shows that the pipeline’s final stage executes, that its output can be audited mechanically, and that the audit must be blind to be worth anything. The dimensions that failed to recover — legibility, cost bearer, propagation pathway — indicate where the toy switch vector does not pin down an instrument, and are therefore examples of where sharper definitions are needed. This is the archetype-to-instrument gap of Section 8.5. Nothing here establishes that the generated instruments would function against a real target, which requires the wargaming and structured expert review identified in Section 8.5; the narratives are analytic artifacts in a synthetic setting, subject to the descriptive-not-prescriptive posture of Section 8.7. 8.7 Ethical Concerns The IGI framework is analytic, not prescriptive. It characterizes how indirect mechanisms produce compliance; it does not recommend their use, and it does not adjudicate the legality or legitimacy of any mechanism the optimizer surfaces, which may be lawful, unlawful, or of ambiguous status under domestic and international law. We flag this deliberately because the model’s structure rewards mechanisms that are deniable and that shift costs onto the target’s own population and firms—designs whose ethical and legal character demands scrutiny that a compliance-maximizing objective does not supply. The same machinery that identifies effective influence mechanisms identifies the mechanisms a defender should anticipate and harden against; the framework’s defensive use (mapping one’s own vulnerabilities to indirect influence) is at least as natural as its offensive use. Operational deployment should pair the compliance objective with explicit legal and normative constraints, treating the optimizer’s output as a hypothesis space to be filtered, not a set of recommendations to be executed. Making the deniability and cost-incidence properties explicit, rather than burying them, is what allows that filtering to occur. 8.8 Limitations and Future Work The switch vector is discrete by design, decomposing mechanism space into a finite set of enumerable configurations. This reflects the interpretability requirement (Section 1): a discrete switch vector lets analysts reason explicitly about configurations and compare them on a common footing. But the discrete structure imposes boundaries a continuous treatment would not; many real mechanisms do not fall cleanly into a single switch value. A natural generalization replaces the discrete switch vector with a continuous latent space, drawing on the variational switching state-space framework of 12. Three further extensions are salient under the mode-switching model. First, the expected-trajectory hazard (Remark 2) should be extended to the full stochastic form with Monte-Carlo over switching times; this reintroduces the Markov-switching character of 13 in a designed rather than inferred form, and lets latent mechanism configurations recovered from historical episodes seed the generative optimizer, uniting the inferential and generative directions. Second, the investment path at\a_t\ should be optimized jointly with s (Section 4.6); because investment intensity drives exposure, the optimal path trades compliance accumulation against dwell time, a genuinely dynamic problem the uniform-investment PoC does not address. We leave these, and the associated calibration agenda, to future work. Third, the model is bilateral. A acts alone and B has no outside options, yet the empirical sanctions literature finds that third parties materially condition outcomes. Allied and adversary states can absorb or offset a sender’s pressure (9; 10), and sender coalitions perform differently from unilateral senders (3). In the present framework a third party would enter as a competing momentum source with its own routing vector, or as a reduction in the effective credibility δ; both are natural extensions of the pressure vector, and neither is developed here. 9 Conclusion We have presented a formal, extensible framework for indirect geoeconomic influence that takes the target’s internal transmission structure seriously and models the moment that structure switches. Its central commitment is that a target’s political economy under influence evolves under mode-dependent rules (permissive before detection, contested after) and that the sender’s mechanism design shapes the transition between them. This inverts the standard regime-switching problem: the transition kernel is designed rather than estimated, and the policy problem becomes steering regime occupancy over a horizon. A structured switch vector decomposes mechanism space, a combinatorial optimizer searches it, and cost-effectiveness metrics place mechanisms on a common frontier. The proof-of-concept demonstrates tractability, not calibration. The clearest next steps are empirical: eliciting the switch-to-parameter and mode-transition mappings, validating dwell-time and durability predictions against historical episodes, and extending the discrete switch space and the expected-trajectory hazard toward their continuous and fully stochastic generalizations. The framework is designed for exactly this iterative refinement. Data and Code Availability The proof-of-concept implementation, the generated instrument descriptions, the blind-classification results, the shuffling key, and the scoring scripts are available from the corresponding author. References Aggarwal and Reddie (2021) V. K. Aggarwal and A. W. 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Schumacher An introduction to hybrid dynamical systems. Vol. 251, Springer. Cited by: §2.3, Remark 2. Zúñiga et al. (2024) N. Zúñiga, S. D. Burton, F. Blancato, and M. Carr The geopolitics of technology standards: historical context for US, EU and chinese approaches. International Affairs 100 (4), p. 1635–1652. Cited by: §1. Appendix A Generation and Classification Prompts This appendix records the prompts used in the proof-of-concept run of the archetype-to-instrument stage (Section 8.6). Both passes used Claude Sonnet 5 on 22 July 2026, each in a fresh incognito session with default decoding settings. Nine generations were produced (three per archetype) and classified in a single blind pass. The generated instruments, the blind classification results, the shuffling key, and the scoring scripts are provided in the supplement. A note on vocabulary. The prompts below are transcribed as executed and therefore use the switch-dimension vocabulary current at the time of the run. In particular they name the second dimension target subsystem with values Government / Private sector / Civil society / Mixed, whereas Table 1 now names it locus of pressure and separates it from target population. The revision does not change the arity of the dimension or the results reported in Section 8.6. A.1 Generation Prompt The prompt below is transcribed as used for the committed generations. The bracketed archetype values were replaced with the six switch values of the mechanism being instantiated. You are assisting with an analytic exercise in a fully fictional setting. There are two fictional polities: Civilization A (the sender) and Civilization B (the target). A seeks to shift B’s dominant resource-allocation policy toward cooperative exchange, but cannot mandate this directly; it must design an indirect mechanism that routes pressure through B’s internal subsystems so that B’s own actors generate the compliance pressure. B has three internal subsystems: its Government (sets official policy, can detect and resist), its Private sector (controls resource infrastructure), and its Civil society (mobility-sensitive population). An abstract mechanism is specified by six structural design choices (a "switch vector"): - Influence timing: Latent | Active | Mixed - whether influence operates before explicit deployment (an unexercised option doing work) or only after. - Target subsystem: Government | Private sector | Civil society | Mixed - which subsystem bears primary pressure. - Propagation pathway: Direct | Cascade | Systemic - how pressure moves through B’s internal system. - Momentum persistence: Low | Medium | High - whether the mechanism self-sustains or requires ongoing investment. - Legibility to B: Transparent | Obscured | Deniable - how easily B’s government identifies and attributes the mechanism. - Cost bearer: A | B | Shared - who absorbs the mechanism’s primary cost. Here is the archetype to instantiate: Influence timing: <FILL> Target subsystem: <FILL> Propagation pathway: <FILL> Momentum persistence: <FILL> Legibility to B: <FILL> Cost bearer: <FILL> Produce a concrete candidate instrument that faithfully instantiates THIS archetype in the Civilization A/B setting. Do not change the design choices; your instrument must reflect them. Return your answer as JSON only, with no prose outside the JSON, in exactly this structure: "mechanism_name": "<short evocative label>", "narrative": "<3-5 sentence description of how the instrument works: who is targeted, what A does, how pressure routes to a policy outcome>", "activation_trigger": "<what sets it in motion>", "expected_behavioral_response": "<what B’s actors do>", "durability_profile": "<what happens if A stops investing>", "self_reported_switches": "influence_timing": "<the value you instantiated>", "target_subsystem": "<...>", "propagation_pathway": "<...>", "momentum_persistence": "<...>", "legibility_to_b": "<...>", "cost_bearer": "<...>" The "self_reported_switches" field must state which switch values your instrument actually reflects, judged on its own merits - not simply copied from the input. If your instrument departs from the requested archetype on any dimension, report the value it actually reflects. A subsequent revision, not used here. Two of the committed generations restate taxonomy vocabulary inside the narrative fields (for example, justifying a durability profile by reference to low momentum persistence). Because such restatement makes a round-trip classification partly circular, the version of the prompt distributed in the supplement adds an instruction forbidding the switch-dimension names and their values in the narrative fields, confining that vocabulary to the self-report. That instruction was added after the committed generations were produced and did not apply to them; results in Section 8.6 reflect the prompt exactly as transcribed above. A.2 Blind Classification Prompt For the blind pass, each generated instrument was reduced to its narrative fields—mechanism name, narrative, activation trigger, expected behavioral response, and durability profile—with the source archetype and the generator’s self-report removed. The nine reduced descriptions were shuffled under a fixed seed and presented one at a time, in a session with no access to the generation pass. You are classifying a described policy instrument against a fixed taxonomy. You will see only a description of a candidate mechanism in a fictional setting (Civilization A influencing Civilization B). Judge only from the description. Assign one value on each of six dimensions: - influence_timing: Latent | Active | Mixed Latent = an offer/capability does its work while unexercised or dormant. Active = pressure only builds through current, live deployment. - target_subsystem: Government | Private sector | Civil society | Mixed. Which of B’s subsystems bears the primary pressure. - propagation_pathway: Direct | Cascade | Systemic Direct = pressure lands on the target actors and stops there. Cascade = it spreads actor-to-actor through peer/social/ competitive imitation. Systemic = it becomes embedded in shared infrastructure/standards affecting the whole system at once. - momentum_persistence: Low | Medium | High Judge from what happens if A stops investing: Low = collapses quickly, High = self-sustaining. - legibility_to_b: Transparent | Obscured | Deniable Transparent = B’s government can plainly identify A’s hand and the demand. Obscured = attribution is possible with effort. Deniable = B’s government cannot attribute it; there is no visible demand from A. NOTE: if A at any point issues a conditional demand or signals that benefits depend on B’s policy, that counts against deniability. - cost_bearer: A | B | Shared Who absorbs the mechanism’s primary cost. Return JSON only, no prose: "switch_vector": "influence_timing": "<value>", "target_subsystem": "<value>", "propagation_pathway": "<value>", "momentum_persistence": "<value>", "legibility_to_b": "<value>", "cost_bearer": "<value>" , "rationale": "<one sentence per dimension, brief>" Here is the instrument to classify: An operational criterion beyond the taxonomy. The rubric above defines legibility partly by whether A issues an explicit conditional demand. That criterion does not appear in the switch vector as specified in Table 1, where the dimension is defined by how readily B identifies and attributes the mechanism. It was added to make the dimension decidable from a narrative alone, and the classifier’s recorded rationales show it carrying most of the weight on that axis. Section 8.6 treats the resulting misclassifications accordingly. Scoring. Recovered switch vectors were compared to the true archetypes dimension by dimension. The comparison is exact-match on the six categorical values; no partial credit is assigned, and the rationale field was not scored. Section 8.6 reports the results, and the scoring script is provided in the supplement.